f11 Chapter Contents
f11 Chapter Introduction
NAG Library Manual

# NAG Library Function Documentnag_sparse_nsym_sort (f11zac)

## 1  Purpose

nag_sparse_nsym_sort (f11zac) sorts the nonzero elements of a real sparse nonsymmetric matrix, represented in coordinate storage format.

## 2  Specification

 #include #include
 void nag_sparse_nsym_sort (Integer n, Integer *nnz, double a[], Integer irow[], Integer icol[], Nag_SparseNsym_Dups dup, Nag_SparseNsym_Zeros zero, Integer istr[], NagError *fail)

## 3  Description

nag_sparse_nsym_sort (f11zac) takes a coordinate storage (CS) representation (see the f11 Chapter Introduction) of a real $n$ by $n$ sparse nonsymmetric matrix $A$, and reorders the nonzero elements by increasing row index and increasing column index within each row. Entries with duplicate row and column indices may be removed, or the values may be summed. Any entries with zero values may optionally be removed.
nag_sparse_nsym_sort (f11zac) also returns istr which contains the starting indices of each row in $A$. This can be used to construct a compressed column storage (CCS) representation of the matrix (see Section 9).

None.

## 5  Arguments

1:     nIntegerInput
On entry: the order of the matrix $A$.
Constraint: ${\mathbf{n}}\ge 1$.
2:     nnzInteger *Input/Output
On entry: the number of nonzero elements in the matrix $A$.
Constraint: ${\mathbf{nnz}}\ge 0$.
On exit: the number of nonzero elements with unique row and column indices.
3:     a[$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nnz}}\right)$]doubleInput/Output
On entry: the nonzero elements of the matrix $A$. These may be in any order and there may be multiple nonzero elements with the same row and column indices.
On exit: the nonzero elements ordered by increasing row index, and by increasing column index within each row. Each nonzero element has a unique row and column index.
4:     irow[$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nnz}}\right)$]IntegerInput/Output
On entry: the row indices of the elements supplied in array a.
Constraint: $1\le {\mathbf{irow}}\left[\mathit{i}\right]\le {\mathbf{n}}$, for $\mathit{i}=0,1,\dots ,{\mathbf{nnz}}-1$.
On exit: the first nnz elements contain the row indices corresponding to the elements returned in array a.
5:     icol[$\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{nnz}}\right)$]IntegerInput/Output
On entry: the column indices of the elements supplied in array a.
Constraint: $1\le {\mathbf{icol}}\left[\mathit{i}\right]\le {\mathbf{n}}$, for $\mathit{i}=0,1,\dots ,{\mathbf{nnz}}-1$.
On exit: the first nnz elements contain the column indices corresponding to the elements returned in array a.
6:     dupNag_SparseNsym_DupsInput
On entry: indicates how any nonzero elements with duplicate row and column indices are to be treated:
• if ${\mathbf{dup}}=\mathrm{Nag_SparseNsym_RemoveDups}$ then duplicate elements are removed;
• if ${\mathbf{dup}}=\mathrm{Nag_SparseNsym_SumDups}$ then the relevant values in array a are summed;
• if ${\mathbf{dup}}=\mathrm{Nag_SparseNsym_FailDups}$ then the function fails on detecting a duplicate.
Constraint: ${\mathbf{dup}}=\mathrm{Nag_SparseNsym_RemoveDups}$, $\mathrm{Nag_SparseNsym_SumDups}$ or $\mathrm{Nag_SparseNsym_FailDups}$.
7:     zeroNag_SparseNsym_ZerosInput
On entry: indicates how any elements with zero values in a are to be treated:
• if ${\mathbf{zero}}=\mathrm{Nag_SparseNsym_RemoveZeros}$ then the entries are removed;
• if ${\mathbf{zero}}=\mathrm{Nag_SparseNsym_KeepZeros}$ then the entries are kept;
• if ${\mathbf{zero}}=\mathrm{Nag_SparseNsym_FailZeros}$ then the function fails on detecting a zero.
Constraint: ${\mathbf{zero}}=\mathrm{Nag_SparseNsym_RemoveZeros}$, $\mathrm{Nag_SparseNsym_KeepZeros}$ or $\mathrm{Nag_SparseNsym_FailZeros}$.
8:     istr[${\mathbf{n}}+1$]IntegerOutput
On exit: ${\mathbf{istr}}\left[\mathit{i}-1\right]-1$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$, is the starting index in the arrays a, irow and icol of each row $i$ of the matrix $A$. ${\mathbf{istr}}\left[n\right]$ contains the number of nonzero elements in $A$ plus one.
9:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

## 6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
On entry, argument dup had an illegal value.
On entry, argument zero had an illegal value.
NE_INT_ARG_LT
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{n}}\ge 1$.
On entry, ${\mathbf{nnz}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{nnz}}\ge 0$.
NE_NON_ZERO_DUP
Nonzero elements have been supplied which have duplicate row and column indices, when ${\mathbf{dup}}=\mathrm{Nag_SparseNsym_FailDups}$.
NE_NONSYMM_MATRIX
A nonzero element has been supplied which does not lie within the matrix $A$,
i.e., one or more of the following constraints has been violated:
$1\le {\mathbf{irow}}\left[\mathit{i}\right]\le {\mathbf{n}}$, $1\le {\mathbf{icol}}\left[\mathit{i}\right]\le {\mathbf{n}}$, for $\mathit{i}=0,1,\dots ,{\mathbf{nnz}}-1$.
NE_ZERO_COEFF
At least one matrix element has been supplied with a zero coefficient value, when ${\mathbf{zero}}=\mathrm{Nag_SparseNsym_FailZeros}$.

Not applicable.

## 8  Parallelism and Performance

Not applicable.

The time taken for a call to nag_sparse_nsym_sort (f11zac) is proportional to nnz.
Note that the resulting matrix may have either rows or columns with no entries. If row $i$ has no entries then ${\mathbf{istr}}\left[i-1\right]={\mathbf{istr}}\left[i\right]$.
It is also possible to use this function to convert between coordinate storage (CS) and compressed column storage (CCS) formats. To achieve this the CS storage format arrays irow and icol must be interchanged in the call to nag_sparse_nsym_sort (f11zac). On exit from nag_sparse_nsym_sort (f11zac), the CCS representation of the matrix is then defined by arrays a, irow and istr. This is illustrated in Section 10.

## 10  Example

This example program reads the CS representation of a real sparse matrix $A$, calls nag_sparse_nsym_sort (f11zac) to reorder the nonzero elements, and outputs the original and the reordered representations.It then calls nag_sparse_nsym_sort (f11zac) again with the alternative ordering, creating a CCS representation which is then passed to a function that computes a matrix norm for that representation.
 $A= 2.00 1.00 0 0 0 0 0 1.00 -1.00 0 4.00 0 1.00 0 1.00 0 0 0 1.00 2.00 0 -2.00 0 0 3.00 .$

### 10.1  Program Text

Program Text (f11zace.c)

### 10.2  Program Data

Program Data (f11zace.d)

### 10.3  Program Results

Program Results (f11zace.r)